Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
9001	(10^56781-31)/3	56781	Serge Batalov	12/2014
9002	7*10^56779+3	56780	Erik Branger	11/2009
9003	12858^13817-13817^12858	56777	Norbert Schneider	11/2018
9004	10^56765+259179	56766	Patrick De Geest	09/2013
9005	10^56765-249497	56765	Patrick De Geest	09/2013
9006	t(188706)	56764	Robert Price	04/2015
9007	2^188551-904327	56760	Paul Bourdelais	11/2012
9008	(64*10^56756+17)/9	56757	Robert Price	09/2015
9009	131101#+146291	56757	Makoto Morimoto	02/2016
9010	2^188539-112519	56756	Enzo Doria	06/2014
9011	6^72927+101	56749	Lelio R Paula	10/2012
9012	20^43617-1603	56748	Enzo Doria	03/2013
9013	(3^118892-8)/91358929	56718	Lelio R Paula	03/2012
9014	13339^13748-13748^13339	56713	Norbert Schneider	09/2018
9015	(509203*2^188338-1)/3	56701	Lelio R Paula	03/2015
9016	20^43567-5623	56682	Enzo Doria	03/2013
9017	2^188234-113183	56665	Enzo Doria	07/2014
9018	(139^26437+1)/140	56653	Richard Fischer	03/2018
9019	(7*2^188215-1)/1497315125	56651	Lelio R Paula	01/2014
9020	(1017*2^188171-1)/35	56647	Lelio R Paula	03/2015
9021	(34*10^56647-7)/9/37/263	56644	Makoto Morimoto	04/2016
9022	(2^188176-1017)/453814543	56638	Lelio R Paula	02/2012
9023	33*10^56634+7	56636	Robert Price	07/2016
9024	(F(31)^9241-F(30)^9241)/F(29)	56634	Wayne Halsdorf	08/2010
9025	14^49413+33	56634	Lelio R Paula	02/2013
9026	3^118680+110	56625	Lelio R Paula	10/2012
9027	(13*10^56624+161)/3	56625	Robert Price	04/2017
9028	(3^118676-2)/7516653263	56613	Lelio R Paula	03/2012
9029	(13*2^188062+1)/17	56613	Lelio R Paula	07/2012
9030	2^188056-1313	56611	Yves Minet	08/2012
9031	20^43510-5583	56608	Enzo Doria	03/2013
9032	2^188032+12285	56604	Lelio R Paula	03/2011
9033	(19*10^56597-43)/3	56598	Robert Price	10/2017
9034	(265*10^56588+17)/3	56590	Robert Price	05/2016
9035	2^187959+5775	56582	Lelio R Paula	03/2011
9036	(5*2^187959+1)/53	56581	Lelio R Paula	07/2012
9037	3*10^56575-13	56576	Robert Price	11/2017
9038	(11*2^187889-1)/351	56559	Lelio R Paula	01/2014
9039	(100049^11311+1)/100050	56553	Faysal YAtim	09/2007
9040	(19*10^56544-1)/9	56545	Serge Batalov	03/2009
9041	20^43447-8923	56526	Enzo Doria	03/2013
9042	10423^14066-14066^10423	56518	Norbert Schneider	11/2018
9043	2^187743-112177	56517	Enzo Doria	06/2014
9044	(F(5879)^47-F(5878)^47)/F(5877)	56502	Wayne Halsdorf	08/2010
9045	5^80831-22	56499	Lelio R Paula	10/2012
9046	5^80828-13166	56497	Enzo Doria	02/2013
9047	7*2^187590-5	56472	Lelio R Paula	03/2014
9048	2^187555+75473	56460	Enzo Doria	04/2016
9049	2^187541-283	56456	Yves Minet	01/2012
9051	(55*10^56453-1)/9	56454	Serge Batalov	03/2009
9050	12933^13730-13730^12933	56454	Norbert Schneider	09/2018
9052	2^187506-1451	56445	Yves Minet	08/2012
9053	189^24794-2	56443	Lelio R Paula	10/2017
9054	13600^13653-13653^13600	56436	Norbert Schneider	08/2018
9055	6^72522+143	56434	Lelio R Paula	10/2012
9056	(15185*2^187452-1)/949	56430	Lelio R Paula	03/2015
9057	2^187390+79	56411	Lelio R Paula	03/2011
9058	2^187386+12909	56409	Lelio R Paula	03/2011
9059	2^187382+613	56408	Jason Earls	04/2008
9060	(34*10^56392-7)/9/37/883/23887	56384	Makoto Morimoto	04/2016
9061	20^43337-9	56383	Lelio R Paula	02/2013
9062	(26*10^56371-173)/3	56372	Robert Price	10/2017
9063	(F(1008)^269-F(1007)^269)/F(1006)	56364	Wayne Halsdorf	08/2010
9065	2^187230+427	56362	Henri Lifchitz	01/2005
9064	11^54121-9480	56362	Enzo Doria	02/2013
9066	10758^13979-13979^10758	56360	Norbert Schneider	09/2018
9067	10635^13996-13996^10635	56359	Norbert Schneider	09/2018
9068	(21*2^187202-1)/43	56354	Lelio R Paula	01/2014
9069	2^187173-91	56345	Lelio R Paula	03/2011
9070	(23*2^187174-1)/20719883	56340	Lelio R Paula	01/2014
9071	2^187125-2833	56331	Yves Minet	09/2014
9072	9*7^66655-4	56331	Lelio R Paula	09/2014
9074	18^44874-97	56330	Lelio R Paula	02/2013
9073	13304^13659-13659^13304	56330	Norbert Schneider	08/2018
9075	60*79^29679+19	56322	Serge Batalov	03/2016
9076	5^80571+56	56317	Lelio R Paula	10/2012
9077	5^80551-22	56303	Lelio R Paula	10/2012
9078	(76*10^56281+41)/9	56282	Robert Price	10/2015
9079	(88*10^56271-43)/9	56272	Robert Price	11/2015
9080	(5*10^56256-119)/3	56257	Robert Price	04/2016
9081	1508^17691+17691^1508	56230	Serge Batalov	05/2014
9082	3^117844-58	56226	Lelio R Paula	10/2012
9083	(19*10^56224+737)/9	56225	Robert Price	10/2017
9084	95^28427+2	56221	Lelio R Paula	05/2013
9085	2^186713+76817	56207	Enzo Doria	05/2016
9086	16534^2505+2505^16534	56196	Hans Havermann	06/2016
9087	14428^7849+7849^14428	56195	Hans Havermann	06/2016
9088	2*10^56194-51	56195	Robert Price	11/2017
9089	14898^5909+5909^14898	56189	Hans Havermann	06/2016
9090	18^44758+95	56184	Lelio R Paula	02/2013
9091	7478^14503-14503^7478	56182	Norbert Schneider	11/2018
9092	2^186555-741	56159	Lelio R Paula	05/2011
9093	(4*10^56156+173)/3	56157	Robert Price	01/2017
9095	(3^117708+7)/447896	56156	Lelio R Paula	03/2012
9094	15711^3752+3752^15711	56156	Hans Havermann	06/2016
9096	(23*2^186549-1)/2429025	56152	Lelio R Paula	01/2014
9097	387^21694+21694^387	56138	Norbert Schneider	08/2014
9098	2^186422+17239	56119	Yves Minet	01/2010
9099	2^186418+4242429	56118	Jason Earls	10/2008
9100	136^26300+135	56113	Norbert Schneider	04/2015
9101	5*2^186392+9	56111	Lelio R Paula	03/2014
9102	14345^8152+8152^14345	56108	Hans Havermann	07/2016
9103	(5*2^186351-1)/39	56097	Lelio R Paula	01/2014
9104	2^186319-541237	56088	Paul Bourdelais	11/2012
9105	2*10^56083-43	56084	Robert Price	07/2017
9106	(16*10^56082-61)/9	56083	Serge Batalov	05/2009
9107	(14*10^56080-143)/3	56081	Robert Price	01/2017
9108	(265*10^56076+17)/3	56078	Robert Price	05/2016
9109	7^66346-50	56069	Lelio R Paula	10/2012
9110	20^43094-33	56067	Lelio R Paula	02/2013
9111	20^43090-1383	56062	Enzo Doria	03/2013
9112	3^117482+2660	56054	Lelio R Paula	10/2012
9113	(22699*2^186193+1)/111	56052	Lelio R Paula	05/2014
9114	(68*10^56042+13)/9	56043	Ray Chandler	09/2010
9115	3*6^71992+5^71992	56022	Mike Oakes	03/2010
9116	13691^12352+12352^13691	56020	Hans Havermann	07/2016
9117	(2^186095+7)/75	56019	Lelio R Paula	02/2012
9118	247^23412+23412^247	56018	Norbert Schneider	08/2014
9119	1839^17156+17156^1839	56008	Serge Batalov	05/2014
9120	13736^11949+11949^13736	56007	Hans Havermann	04/2016
9121	(5*2^186036-1)/11	56003	Lelio R Paula	01/2014
9122	(299*10^55998-17)/3	56000	Robert Price	01/2017
9123	p(12103)#/2-128	55994	Robert Price	05/2017
9124	2^186003-174337	55993	Gary Barnes	09/2009
9125	(2^186010+78557)/123	55993	Lelio R Paula	05/2012
9126	20^43037-93	55993	Lelio R Paula	02/2013
9127	16375^2626+2626^16375	55991	Hans Havermann	03/2016
9128	11083^13842-13842^11083	55987	Norbert Schneider	11/2018
9129	15631^3816+3816^15631	55985	Hans Havermann	03/2016
9130	21^42335-2	55977	Lelio R Paula	08/2013
9131	Phi(64736,139)	55959	Enzo Doria	07/2012
9132	15215^4762+4762^15215	55958	Hans Havermann	03/2016
9133	19317^788+788^19317	55953	Anatoly F. Selevich	12/2006
9134	13582^13165+13165^13582	55950	Hans Havermann	08/2016
9135	(78557*2^185842+1)/189	55947	Lelio R Paula	06/2014
9136	11867^13730-13730^11867	55941	Norbert Schneider	09/2018
9137	15^47562-86	55938	Lelio R Paula	02/2013
9138	4*10^55932+91	55933	Robert Price	11/2017
9139	3^117222+4	55930	Lelio R Paula	03/2012
9140	24^40519-23^40519	55925	Robert Price	07/2012
9141	13636^12623+12623^13636	55924	Hans Havermann	07/2016
9142	2^185767-99	55922	Lelio R Paula	03/2011
9143	(19*2^185750-1)/15	55917	Lelio R Paula	01/2014
9145	15^47542-58	55914	Lelio R Paula	02/2013
9144	52211!4+2	55914	Robert Price	08/2017
9146	20^42973-5583	55910	Enzo Doria	03/2013
9147	4*10^55906+21	55907	Robert Price	08/2016
9148	2^185713-111	55906	Lelio R Paula	03/2011
9149	13^50174+88	55891	Lelio R Paula	01/2013
9150	14569^6846+6846^14569	55879	Hans Havermann	08/2016
9151	Pell-LucasQ(145969)/2	55874	Eric W. Weisstein	08/2006
9152	3^117087-80	55865	Lelio R Paula	10/2012
9153	(7*10^55851-43)/9	55851	Robert Price	10/2014
9154	2^185519-169	55847	Lelio R Paula	03/2011
9155	7^66074+10	55840	Lelio R Paula	10/2012
9156	(19*10^55833-49)/3	55834	Robert Price	02/2017
9157	(2*10^55834-59)/3	55834	Robert Price	05/2017
9158	2^185463-4237	55830	Yves Minet	08/2018
9159	12^51732+5	55829	Lelio R Paula	01/2013
9160	11252^13779-13779^11252	55822	Norbert Schneider	10/2018
9161	3*2^185429+7	55821	Lelio R Paula	03/2014
9162	(60^31393+1)/61	55820	Paul Bourdelais	08/2017
9163	(9787*2^185420-1)/381	55819	Lelio R Paula	04/2015
9164	14427^7396+7396^14427	55819	Hans Havermann	08/2016
9165	10^55811+21	55812	Robert Price	01/2011
9166	10^55811-74103	55811	Patrick De Geest	12/2012
9167	11^53591-1530	55810	Enzo Doria	11/2012
9168	(5^79841-5^39921+1)/15334159	55800	Lelio R Paula	09/2017
9169	2^185355-2145	55798	Lelio R Paula	03/2011
9170	14531^6912+6912^14531	55794	Hans Havermann	07/2016
9171	2^185327-1615	55789	Lelio R Paula	03/2011
9172	2^185280-12779	55775	Enzo Doria	10/2012
9173	15504^3955+3955^15504	55771	Hans Havermann	07/2016
9174	(2*10^55762-59)/3	55762	Robert Price	05/2017
9175	5^79770-44	55757	Lelio R Paula	10/2012
9176	18^44416-85	55755	Lelio R Paula	02/2013
9177	2^185208-459995	55754	Enzo Doria	06/2015
9178	2^185200+1185	55751	Lelio R Paula	03/2011
9179	(536*10^55748-23)/9	55750	Robert Price	11/2017
9180	7^65964+6^(65964-1)	55747	Robert Price	03/2016
9181	2^185151-237157	55737	Gary Barnes	09/2009
9182	110017^11055-102	55734	Enzo Doria	07/2012
9183	14754^5987+5987^14754	55729	Hans Havermann	07/2016
9184	12591^13592-13592^12591	55729	Norbert Schneider	07/2018
9185	40090!3-9	55711	Robert Price	09/2014
9186	9*10^55707+89	55708	Robert Price	11/2016
9187	2^185023-2257	55698	Yves Minet	06/2009
9188	18628^977+977^18628	55696	Anatoly F. Selevich	01/2007
9189	2^185006-93	55693	Lelio R Paula	03/2011
9190	2^185003-2515	55692	Yves Minet	07/2014
9191	2^184992-78557	55689	Jorge Menendez	02/2018
9192	3*10^55679+37	55680	Robert Price	10/2017
9193	6^71524-19	55657	Lelio R Paula	10/2012
9194	2^184872-2195	55653	Yves Minet	08/2013
9195	507^20572+20572^507	55648	Norbert Schneider	06/2016
9196	(86*10^55645-311)/9	55646	Robert Price	10/2017
9197	134^26151-133	55626	Norbert Schneider	03/2015
9198	15340^4221+4221^15340	55614	Hans Havermann	07/2016
9199	27743!2+2	55612	Robert Price	01/2013
9200	20^42744+81	55612	Lelio R Paula	02/2013
9201	14609^6406+6406^14609	55611	Hans Havermann	07/2016
9202	2^184724-112883	55608	Enzo Doria	06/2014
9203	13507^13074+13074^13507	55601	Hans Havermann	07/2016
9204	2^184689+129	55597	Lelio R Paula	03/2011
9205	(9179*2^184672-1)/193	55594	Lelio R Paula	03/2015
9206	(22*10^55592-19)/3	55593	Robert Price	02/2017
9207	Phi(59984,89)	55582	Enzo Doria	05/2012
9208	8815^14088-14088^8815	55581	Norbert Schneider	11/2018
9209	11^53368+16	55578	Lelio R Paula	01/2013
9210	20^42717-1923	55577	Enzo Doria	03/2013
9211	117^26870+26870^117	55573	Serge Batalov	05/2014
9212	12^51488+55	55565	Lelio R Paula	01/2013
9213	(44*10^55558-17)/9	55559	Robert Price	06/2015
9214	(2*10^55559-23)/3	55559	Robert Price	09/2017
9215	10^55555+32857	55556	Patrick De Geest	06/2010
9216	10^55555-136721	55555	Patrick De Geest	06/2010
9217	(11*2^184541-1)/351	55551	Lelio R Paula	01/2014
9218	20^42696-2043	55549	Enzo Doria	03/2013
9219	(35*10^55547-737)/9	55548	Robert Price	11/2017
9220	(2*10^55544+1)/3	55544	Serge Batalov	06/2009
9221	(-lucasV(1,2,369056)+2)/(389109*457)	55542	Mike Oakes	04/2017
9222	5003^15013-160	55537	Enzo Doria	07/2012
9223	39^34896-2	55522	Lelio R Paula	08/2013
9224	(6^71345-61)/5	55517	Lelio R Paula	05/2014
9225	2^184407-3019	55513	Yves Minet	10/2014
9226	(43*10^55512-61)/9	55513	Robert Price	06/2015
9227	20^42667-843	55512	Enzo Doria	03/2013
9228	133^26134-132	55505	Norbert Schneider	03/2015
9229	(31*2^184378-1)/711	55502	Lelio R Paula	01/2014
9230	9*7^65667-4	55497	Lelio R Paula	09/2014
9231	2^184342-173	55493	Lelio R Paula	03/2011
9232	15^47182+92	55491	Lelio R Paula	02/2013
9233	5^79378+6	55483	Lelio R Paula	10/2012
9234	581^20068+20068^581	55472	Norbert Schneider	06/2016
9235	(2^184232+1)/257	55457	Donovan Johnson	03/2005
9236	18^44177-1415	55455	Enzo Doria	03/2013
9237	2^184203-2797867	55451	Enzo Doria	04/2016
9238	2^184189+17	55447	Lelio R Paula	03/2011
9239	2^184183+26123	55445	Yves Minet	01/2010
9240	Phi(77077,10)	55441	Ray Chandler	05/2009
9241	2^184141-113251	55432	Enzo Doria	07/2014
9242	2^184093-504613	55418	Gary Barnes	09/2009
9243	6517^14528-14528^6517	55411	Norbert Schneider	12/2018
9244	(lucasV(1,2,368167)+2)/(1111031307*5647)	55404	Mike Oakes	04/2017
9245	2^184044-111269	55403	Enzo Doria	05/2014
9246	14051^8766+8766^14051	55401	Hans Havermann	07/2016
9247	98^27819+27819^98	55394	Serge Batalov	05/2014
9248	(178*10^55390-7)/9	55392	Robert Price	08/2017
9249	58046^9+9^58046	55390	Andrey Kulsha	02/2004
9250	7^65536+2*59232-2	55385	Jiahao He	07/2017

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PRP Records

Probable Primes Top 10000

(252402 PRPs in the top)